Polarized Light in the Cosmic Microwave Background: WMAP Three-year Results

Polarized Light in the Polarized Light in the Cosmic Microwave Cosmic Microwave

Background: WMAP Background: WMAP Three-year ResultsThree-year Results

Eiichiro Komatsu (UT Austin)Eiichiro Komatsu (UT Austin)Colloquium at U. of MinnesotaColloquium at U. of Minnesota

November 3, 2006November 3, 2006

Full Sky Microwave MapFull Sky Microwave Map

Penzias & Wilson, 1965Uniform, “Fossil” Light from the Big Bang

-Isotropic

-Unpolarized

Galactic CenterGalactic Anti-center

A. Penzias & R. Wilson, 1965A. Penzias & R. Wilson, 1965

CMBT = 2.73 K

Helium SuperfluidityT = 2.17 K

COBE/FIRAS, 1990COBE/FIRAS, 1990Perfect blackbody = Thermal equilibrium = Big Bang

COBE/DMR, 1992COBE/DMR, 1992

Gravity is STRONGER in cold spots: T/T~

Isotropic?

COBE, “Followed-up” by WMAPCOBE, “Followed-up” by WMAPCOBE

WMAP

COBE1989

WMAP2001

[COBE’s] measurements also marked the inception of cosmology as a precise science. It was not long before it was followed up, for instance by the WMAP satellite, which yielded even clearer images of the background radiation.

Press Release from the Nobel Foundation

David Wilkinson (1935~2002)David Wilkinson (1935~2002)

• Science Team Meeting, July, 2002• Plotted the “second point” (3.2cm) on the CMB spectrum

– The first confirmation of a black-body spectrum (1966)• Made COBE and MAP happen and be successful• “Father of CMB Experiment”• MAP has become WMAP in 2003

So, It’s Been Three Years Since So, It’s Been Three Years Since The First Data Release in 2003. The First Data Release in 2003.

What Is New Now?What Is New Now?

POLARIZATION DATA!!POLARIZATION DATA!!Not only anisotropic, but also polarizNot only anisotropic, but also polariz

ed.ed.

The Wilkinson Microwave The Wilkinson Microwave Anisotropy ProbeAnisotropy Probe

• A microwave satellite working at L2• Five frequency bands

– K (22GHz), Ka (33GHz), Q (41GHz), V (61GHz), W (94GHz)– Multi-frequency is crucial for cleaning the Galactic emission

• The Key Feature: Differential Measurement– The technique inherited from COBE– 10 “Differencing Assemblies” (DAs)– K1, Ka1, Q1, Q2, V1, V2, W1, W2, W3, & W4, each consisting of two

radiometers that are sensitive to orthogonal linear polarization modes.

• Temperature anisotropy is measured by single difference.• Polarization anisotropy is measured by double difference.

POLARIZATION DATA!!

WMAP Three Year PapersWMAP Three Year Papers

K band (22GHz)K band (22GHz)

Ka Band (33GHz)Ka Band (33GHz)

Q Band (41GHz)Q Band (41GHz)

V Band (61GHz)V Band (61GHz)

W Band (94GHz)W Band (94GHz)

The Angular Power SpectrumThe Angular Power Spectrum• CMB temperature anisotropy is very close to

Gaussian (Komatsu et al., 2003); thus, its spherical harmonic transform, alm, is also Gaussian.

• Since alm is Gaussian, the power spectrum:

completely specifies statistical properties of CMB.

*lmlml aaC

WMAP 3-yr Power SpectrumWMAP 3-yr Power Spectrum

What Temperature Tells UsWhat Temperature Tells Us

Distance to z~1100

Baryon-to-Photon Ratio

Matter-Radiation Equality Epoch

Dark Energy/New Physics?

CMB to CosmologyCMB to Cosmology

&Third

Baryon/Photon Density Ratio

Low Multipoles (ISW)

K Band (23 GHz)K Band (23 GHz)Dominated by synchrotron; Note that polarization direction is perpendicular to the magnetic field lines.

Ka Band (33 GHz)Ka Band (33 GHz)Synchrotron decreases as -3.2 from K to Ka band.

Q Band (41 GHz)Q Band (41 GHz)We still see significant polarized synchrotron in Q.

V Band (61 GHz)V Band (61 GHz)The polarized foreground emission is also smallest in V band. We can also see that noise is larger on the ecliptic plane.

W Band (94 GHz)W Band (94 GHz)While synchrotron is the smallest in W, polarized dust (hard to see by eyes) may contaminate in W band more than in V band.

Polarization MaskPolarization Mask

fsky=0.743

Jargon: E-mode and B-modeJargon: E-mode and B-mode• Polarization has directions!• One can decompose it into a divergence-like

“E-mode” and a vorticity-like “B-mode”.

E-mode B-mode

Seljak & Zaldarriaga (1997); Kamionkowski, Kosowsky, Stebbins (1997)

Polarized Light Filtered

Polarized Light Un-filtered

Physics of CMB PolarizationPhysics of CMB Polarization• Thomson scattering generates polarization, if and only if…

– Temperature quadrupole exists around an electron– Where does quadrupole come from?

• Quadrupole is generated by shear viscosity of photon-baryon fluid.

electronisotropic

anisotropic

no net polarization

net polarization

Boltzmann EquationBoltzmann Equation

• Temperature anisotropy, , can be generated by gravitational effect (noted as “SW” = Sachs-Wolfe, 1967)

• Linear polarization (Q & U) is generated only by scattering (noted as “C” = Compton scattering).

• Circular polarization (V) is not generated by Thomson scattering.

Primordial Gravity WavesPrimordial Gravity Waves• Gravity waves also create quadrupolar temp

erature anisotropy -> Polarization• Most importantly, GW creates B mode.

Power SpectrumPower SpectrumScalar T

Tensor T

Scalar E

Tensor E

Tensor B

Polarization From ReionizationPolarization From Reionization• CMB was emitted at z~1100.• Some fraction of CMB was re-scattered in a reionized u

niverse.• The reionization redshift of ~11 would correspond to 3

65 million years after the Big-Bang.

z=1100, ～ 1

z～ 11, ～0.1

First-star formation

z=0

IONIZED

REIONIZED

NEUTRAL

e-

e-e-

e-

e-e- e-

e-e-e-

e-

e-

e- e- e-

Measuring Optical DepthMeasuring Optical Depth• Since polarization is generated by scattering, the

amplitude is given by the number of scattering, or optical depth of Thomson scattering:

which is related to the electron column number density as

Polarization from ReioniazationPolarization from Reioniazation

“Reionization Bump”

2

• Outside P06– EE (solid)– BB (dashed)

• Black lines– Theory EE

• tau=0.09– Theory BB

• r=0.3

• Frequency = Geometric mean of two frequencies used to compute Cl

Masking Is Not Enough: Masking Is Not Enough: Foreground Must Be CleanedForeground Must Be Cleaned

Rough fit to BB FG in 60GHz

Clean FGClean FG

•Only two-parameter fit!

•Dramatic improvement in chi-squared.

•The cleaned Q and V maps have the reduced chi-squared of ~1.02 per DOF=4534 (outside P06)

BB consistent with zero after FG removal.

3-sigma detection of EE.

The “Gold” multipoles: l=3,4,5,6.

Parameter Determination: Parameter Determination: First Year vs Three YearsFirst Year vs Three Years

• The simplest LCDM model fits the data very well.– A power-law primordial power spectrum– Three relativistic neutrino species– Flat universe with cosmological constant

• The maximum likelihood values very consistent– Matter density and sigma8 went down slightly

Null TestsNull Tests• It’s very powerful to have

three years of data.– Year-year differences must

be consistent with zero signal.

• yr1-yr2, yr2-yr3, and yr3-yr1• We could not do this null test

for the first year data.

– We are confident that we understand polarization noise to a couple of percent level.

• Statistical isotropy– TB and EB must be

consistent with zero.

• Inflation prior…– We don’t expect 3-yr data

to detect any BB.

Data Combination (l<23)Data Combination (l<23)• We used Ka, Q, V, and W for the 1-yr TE analysis. • We use only Q and V for the 3-yr polarization analysis.

– Despite the fact that all of the year-year differences at all frequencies have passed the null tests, the 3-yr combined power spectrum in W band shows some anomalies.

• EE at l=7 is too high. We have not identified the source of this anomalous signal. (FG is unlikely.)

• We have decided not to use W for the 3-yr analysis.– The residual synchrotron FG is still a worry in Ka.

• We have decided not to use Ka for the 3-yr analysis.

• KaQVW is ~1.5 times more sensitive to tau than QV.– Therefore, the error reduction in tau by going from the first-year (KaQVW) t

o three-year analysis (QV) is not as significant as one might think from naïve extrapolation of the first-year result.

– There is also another reason why the three-year error is larger (and more accurate) – next slide.

Correlated NoiseCorrelated Noise• At low l, noise is not white.• 1/f noise increases noise at lo

w l– See W4 in particular.

• Scan pattern selectively amplifies the EE and BB spectra at particular multipoles.– The multipoles and amplitude

of noise amplification depend on the beam separation, which is different from DA to DA.

Red: white noise model (used in the first-year analysis)

Black: correlated noise model (3-yr model)

Low-l TE Data: Comparison between Low-l TE Data: Comparison between 1-yr and 3-yr1-yr and 3-yr

• 1-yr TE and 3-yr TE have about the same error-bars.– 1yr used KaQVW and wh

ite noise model• Errors significantly und

erestimated.• Potentially incomplete

FG subtraction.– 3yr used QV and correla

ted noise model• Only 2-sigma detection

of low-l TE.

High-l TE DataHigh-l TE Data

• The amplitude and phases of high-l TE data agree very well with the prediction from TT data and linear perturbation theory and adiabatic initial conditions. (Left Panel: Blue=1yr, Black=3yr)

Phase Shift

Am

pli

tud

e

High-l EE DataHigh-l EE Data

• When QVW are coadded, the high-l EE amplitude relative to the prediction from the best-fit cosmology is 0.95 +- 0.35.

• Expect ~4-5sigma detection from 6-yr data.

WMAP: QVW combined

1st year vs 3rd year1st year vs 3rd year• Tau is almost entirely de

termined by the EE from the 3-yr data.– TE adds very little.

• Dotted: Kogut et al.’s stand-alone tau analysis from TE

• Grey lines: 1-yr full analysis (Spergel et al. 2003)

Tau is Constrained by EETau is Constrained by EE• The stand-alone analysis of EE data gives

– tau = 0.100 +- 0.029

• The stand-alone analysis of TE+EE gives– tau = 0.092 +- 0.029

• The full 6-parameter analysis gives– tau = 0.093 +- 0.029 (Spergel et al.; no SZ)

• This indicates that the stand-alone EE analysis has exhausted most of the information on tau contained in the polarization data.– This is a very powerful statement: this immediately implies that th

e 3-yr polarization data essentially fixes tau independent of the other parameters, and thus can break massive degeneracies between tau and the other parameters.

Degeneracy Finally Broken: Degeneracy Finally Broken: Negative Tilt & Low Fluctuation Negative Tilt & Low Fluctuation

AmplitudeAmplitudeDegeneracy Line from Temperature Data Alone

Polarization Data Nailed Tau

Temperature Data Constrain “8exp(-)”

Lower

Polarization Nailed Tau

Lower 3rd peak

Constraints on GWConstraints on GW• Our ability to

constrain the amplitude of gravity waves is still coming mostly from the temperature spectrum.– r<0.55 (95%)

• The B-mode spectrum adds very little.

• WMAP would have to integrate for at least 15 years to detect the B-mode spectrum from inflation.

What Should WMAP Say What Should WMAP Say About Inflation Models?About Inflation Models?

Hint for ns<1

Zero GW The 1-d marginalized constraint from WMAP alone is ns=0.96+-0.02.

GW>0The 2-d joint constraint still allows for ns=1.

What Should WMAP Say What Should WMAP Say About Flatness?About Flatness?

Flatness, or very low Hubble’s constant?

If H=30km/s/Mpc, a closed universe with Omega=1.3 w/o cosmological constant still fits the WMAP data.

What Should WMAP Say What Should WMAP Say About Dark Energy?About Dark Energy?

Not much!

The CMB data alone cannot constrain w very well. Combining the large-scale structure data or supernova data breaks degeneracy between w and matter density.

What Should WMAP Say What Should WMAP Say About Neutrino Mass?About Neutrino Mass?

3.04)

• Understanding of– Noise,– Systematics,– Foreground, and

• Analysis techniques • have significantly improved

from the first-year release.

• A simple LCDM model fits both the temperature and polarization data very well.

• To-do list for the next data release (now working on the 5-year data)

• Understand FG and noise better.

• We are still using only 1/2 of the polarization data.

• These improvements, combined with more years of data, would further reduce the error on tau.

• Full 3-yr would give delta(tau)~0.02

• Full 6-yr would give delta(tau)~0.014 (hopefully)

• This will give us a better estimate of the tilt, and better constraints on inflation.

SummarySummary

•Tau=0.09+-0.03